Field of the Invention
The invention concerns a method for the reconstruction of image data for at least two different chemical substance types in a defined region of an examination object from raw data that has been ascertained for the defined region at different echo times in a magnetic resonance scan. Furthermore, the invention concerns a method for ascertaining image data for at least two different chemical substance types in a defined region of an examination object by execution of an imaging magnetic resonance scan. The invention also concerns an image processing computer for the reconstruction of image data for at least two different chemical substance types in a defined region of an examination object from raw data has been ascertained for the defined region at different echo times in a magnetic resonance scan. Furthermore, the invention concerns a magnetic resonance system having such an image processing computer.
Description of the Prior Art
In a magnetic resonance scan wherein raw data generated are acquired, by operation of scanner, a magnetic resonance from a region of the inside of the body of an examination object, the body or the body part to be examined must first be exposed to an optimally homogeneous static basic magnetic field in the scanner, usually called the B0 field. The nuclear spins in the body are thereby oriented parallel to the direction of the B0 field (conventionally called the z direction). In addition, radio-frequency pulses (RF pulses) are radiated into the examination object using suitable radio-frequency antennae whose frequency is in the region of the resonance frequency, what is known as the Larmor frequency, of the nuclei to be excited in the present magnetic field. These radio-frequency pulses cause the spins of the relevant nuclei, usually hydrogen nuclei, to be excited in the examination object such that they are deflected by an amount known as an “excitation flip angle” from their position of equilibrium parallel to the basic magnetic field B0. The nuclear spins then precess around the z direction and gradually relax again, with the relaxation being dependent on the molecular surroundings in which the excited nucleus is located. The magnetic resonance signals generated during relaxation are received as raw data by radio-frequency receiving antennae, and are entered at respective entry points into a memory. The data in the memory are called k-space, and magnetic resonance images (image data) are reconstructed on the basis of the acquired raw data in k-space. Spatial encoding of the magnetic resonance signals occurs with the activation of rapidly-switched gradient magnetic fields that are superimposed on the basic magnetic field during emission of the magnetic resonance radio-frequency pulses and/or the acquisition of the raw data.
A generally known basic problem in the acquisition of raw data is that the excited nuclei in the body tissue do not have a uniform resonance frequency in the magnetic field. Instead these can differ for different tissue types or substance types according to their chemical surroundings. This is conventionally called a chemical shift. As used herein, a substance type (or substance for short) means any type of predefined chemical substance or any type of nucleus in an atom or molecule having specific magnetic resonance behavior. A typical example of different substance types are the substance types fat and water. A substance type can contain multiple components that have (slightly) different resonance frequencies. For example, the substance type, as described in more detail below, can be described by a chemical spectral model having a number of peaks with respect to the resonance frequency. Different substance types thus also encompass within their meaning more complex chemical compounds or mixtures that have different components and possibly also different resonance frequencies, but combine to form a characteristic spectrum. Particularly relevant in magnetic resonance imaging is the chemical shift of fat tissue in relation to the conventionally excited water, since fat occurs in significant quantities in many regions of the body. The chemical shift between fat tissue and water is approximately 3.4 ppm.
Various methods are known to create separate magnetic resonance images for different substance types, for example to generate separate water and fat images. A typical method for this purpose is what is known as the two-point Dixon method. For this purpose, raw data acquired, using suitable magnetic resonance sequences, during two different echoes, for example two different gradient echoes or spin echoes, with these echoes differing in their echo time.
For example, for two chemical substance types the complex-value signals S1(x) and S2(x) at one image point having the coordinates v can be represented by the equationsS1(x)=(W(x)+c1F(x))eiφ1(x)  (1)S2(x)=(W(x)+c2F(x))eiφ2(x)  (2)
Here W(x) again denotes the water and F(x) the fat content at the respective image point. Basically W(x) and F(x) can also denote any other chemical substance types. S1(x) and S2(x) are the intensity values for the first echo and for the second echo at the respective image point. In the case of two-dimensional image data, an image point here and below means a pixel, and in the case of three-dimensional image data a voxel. For shorthand, x is used to represent the coordinates of the image point, which are multi-dimensional. Solely for simplicity, the conventional notation for water and fat will be used since this is the most common application. In the equations (1) and (2) c1 and c2 are complex-value coefficients that depend on the echo time and the spectrum of the second chemical substance (i.e. here as an example the spectrum of the fat F). Due to the dephasing each of the recorded images is slightly different, even if the same region is acquired in each case, since each chemical substance oscillates slightly differently. In equations (1) and (2), for simplicity, it is assumed, moreover, that a complicated spectrum exists only for one of the two chemical substance types, here the fat F. This method may also be expanded to other substance types. In this case, a complex-value coefficient must likewise be inserted before the W component in equations (1) and (2). In addition, it is assumed in equations (1) and (2) that the phases or phase rotations of the signals are each given by φ1(x) and φ2(x).
The exponents φ1 and φ2 in equations (1) and (2) may be generally described as follows:Φ(t,x)=Ω(x)·t±ΦEC(x)+ϕ(t,x)  (3)
Here Φ is the phase accumulation at a specific location at a specific time, Ω(x) the local off-center frequency, ΦEC(x) the phase accumulation of opposed polarities due to eddy currents and φ(t,x) the phase after excitation. The relaxation over time is modeled by a positive imaginary part of Ω(x).
Various algorithms are known to generate the water image W and the fat image F from the acquired signals using equations (1) and (2). Due to possible field inhomogeneities, gradient delays, eddy currents, etc. it is very important for the two-point Dixon method to determine the global phase rotation (p between the echo times per image point and to then take it into account in the reconstruction. For this purpose, it is conventionally assumed that the variation in the phase rotation is spatially weak, i.e. that the variation between adjacent image points is for example <180°. The conventional solution methods are based on iteration methods with which solutions to equations 1 and 2 are ascertained.
In many cases, multi-echo sequences are used in the imaging method, in which raw data are acquired at many different echo times TE,e, where e=1, . . . , NE with NE equal to the number of echoes. Often the raw data acquired per echo are undersampled, meaning that not every available data entry point in k-space is filled. This means the image data has to be reconstructed from raw data of a number of echoes. The number of echoes increases the amount of information, and therefore provides a possibility for compensating the undersampling. The phases of the signals between the individual echo times are subject to changing spatially according to equation (3), however, which must be taken into account when ascertaining the image data of the individual chemical substances.
In the case of the signal model according to equations (1) and (2) or an equation system expanded to a number of echoes, when the development of the phase accumulation over time and the disruptive effects, as are described by equation (3), are to be taken into account, then a non-linear optimization problem is conventionally solved, which converges only slowly, and it is not guaranteed that there will be a convergence in the sense of a global minimum.